The discussion revolves around Haag's theorem and its implications for the nature of free and interacting fields in quantum field theory. Participants explore the mathematical foundations and interpretations of Haag's theorem, particularly focusing on the distinction between free fields and interacting fields, as well as the relevance of different approaches to quantum field theory.
Participants express differing views on the implications of Haag's theorem and its relationship to various approaches in quantum field theory. There is no consensus on whether Haag's conclusions apply uniformly across different frameworks.
Participants discuss the limitations and assumptions inherent in Haag's theorem, particularly regarding the mathematical treatment of free and interacting fields and the implications of unitarily inequivalent representations.
That's not quite what Haag's theorem says. A free field and an interacting field are different things, and one cannot "become" the other, regardless of what Haag's theorem or any other mathematical result says.lindberg said:according to Haag's theorem, a free field cannot become an interacting one?
Wasn't Haag's conclusion extended later to other approaches?PeterDonis said:To someone who is used to the usual way of modeling interacting fields as perturbations of free fields, this seems like a problem; but there are other approaches to quantum field theory, such as the algebraic approach, in which it is not a problem at all.
Given that the whole point of the algebraic approach to QFT is to be able to deal with unitarily inequivalent representations, showing that the algebraic approach leads to unitarily inequivalent representations isn't much of an issue.lindberg said:Wasn't Haag's conclusion extended later to other approaches?